U.S. State Department spokeswoman Jen Psaki noted Russia made a similar announcement last week that turned out to be untrue.

Earlier on May 19, Putin's office said he had ordered military forces near the Ukrainian border to return to their permanent barracks after ending spring exercises.

NATO estimates that Russia has some 40,000 troops along the border with Ukraine.

Meanwhile, the chief of the general staff of Russia's armed forces said NATO's increased military activity in the region was not helping to calm tensions in eastern Ukraine.

Valery Gerasimov's comments came as a senior UN official expressed serious concerns about the conditions under which Ukrainians were to go to the polls on May 25.

Speaking to Reuters, Ivan Simonovic, the UN Assistant Secretary-General for Human Rights, said the UN had received reports of abductions and intimidation of election officials in eastern Ukraine and fears many people will flee the region due to a mounting sense of lawlessness.

Ukrainian Interior Minister Arsen Avakov admitted the security situation in the eastern regions of Donetsk and Luhansk -- where pro-Russian separatists have declared "people's republics" -- meant "there is no way to hold elections in a normal way."

Meanwhile, Russian Foreign Minister Sergei Lavrov on May 19 said Moscow's relations with the European Union and NATO require "serious rethinking" due to the Ukraine crisis.

Lavrov also called on the Organization for Security and Cooperation in Europe (OSCE) to assist in the release of two Russian television journalists apparently detained in eastern Ukraine.

The two were reportedly held by Ukrainian security forces near the flashpoint city of Kramatorsk.

He also said Slovakia's decision to allow for reverse gas flows to Ukraine does not violate its agreements with Gazprom and the Russian government. He made the comments in Moscow after talks with visiting Slovak Foreign Minister Miroslav Lajcak.

Russia is threatening to halt gas supplies to Ukraine because of Kyiv's failure to pay for past deliveries.